The present invention relates generally to separating individual source signals from a mixture of the source signals and more specifically to a method and apparatus for separating convolutive mixtures of source signals.
A classic problem in signal processing, best known as blind source separation, involves recovering individual source signals from a mixture of those individual signals. The separation is termed `blind` because it must be achieved without any information about the sources, apart from their statistical independence. Given L independent signal sources (e.g., different speakers in a room) emitting signals that propagate in a medium, and L' sensors (e.g., microphones at several locations), each sensor will receive a mixture of the source signals. The task, therefore, is to recover the original source signals from the observed sensor signals. The human auditory system, for example, performs this task for L'=2. This case is often referred to as the `cocktail party` effect; a person at a cocktail party must distinguish between the voice signals of two or more individuals speaking simultaneously.
In the simplest case of the blind source separation problem, there are as many sensors as signal sources (L=L') and the mixing process is instantaneous, i.e., involves no delays or frequency distortion. In this case, a separating transformation is sought that, when applied to the sensor signals, will produce a new set of signals which are the original source signals up to normalization and an order permutation, and thus statistically independent. In mathematical notation, the situation is represented by ##EQU1##
where g is the separating matrix to be found, v(t) are the sensor signals and u(t) are the new set of signals.
Significant progress has been made in the simple case where L=L' and the mixing is instantaneous. One such method, termed independent component analysis (ICA), imposes the independence of u(t) as a condition. That is, g should be chosen such that the resulting signals have vanishing equal-time cross-cumulants. Expressed in moments, this condition requires that EQU &lt;u.sub.i (t).sup.m u.sub.j (t).sup.n &gt;=&lt;u.sub.i (t).sup.m &gt;&lt;u.sub.j (t).sup.n &gt;
for i=j and any powers m, n; the average taken over time t. However, equal-time cumulant-based algorithms such as ICA fail to separate some instantaneous mixtures such as some mixtures of colored Gaussian signals, for instance.
The mixing in realistic situations is generally not instantaneous as in the above simplified case. Propagation delays cause a given source signal to reach different sensors at different times. Also, multi-path propagation due to reflection or medium properties creates multiple echoes, so that several delayed and attenuated versions of each signal arrive at each sensor. Further, the signals are distorted by the frequency response of the propagation medium and of the sensors. The resulting `convolutive` mixtures cannot be separated by ICA methods.
Existing ICA algorithms can separate only instantaneous mixtures. These algorithms identify a separating transformation by requiring equal-time cross-cumulants up to arbitrarily high orders to vanish. It is the lack of use of non-equal-time information that prevents these algorithms from separating convolutive mixtures and even some instantaneous mixtures.
As can be seen from the above, there is need in the art for an efficient and effective learning algorithm for blind separation of convolutive, as well as instantaneous, mixtures of source signals.